Posterity has not been kind to Anthony Asquith. If he is remembered at all today, it is as much for his family connections as for his movies. He was the son of a prime minister and the great-uncle of actress Helena Bonham Carter. When he was six years old, he moved house - to 10 Downing Street. His father, Herbert Asquith, had just formed the Liberal government of 1908; his mother, Margot, was a celebrated society figure. It was an unlikely background for a future film-maker. At that time, cinema was not a respectable profession. Asquith himself famously described it as the bastard offspring of "an unholy liaison between the magic lantern and the novelette".

Asquith's best-known films (The Way to the Stars, The Browning Version, The Winslow Boy, The Importance of Being Earnest, and so on) pop up regularly on television, but beyond acknowledging the "skill and stylistic polish" that he brought to these pictures, critics rarely give him much credit. "He was a dull, journeyman supervisor of proven theatrical properties," says David Thomson in his Biographical Dictionary of Cinema, before going on to accuse Asquith of making "addled movies that accepted a 1920s notion of the intrinsic appeal of wealthy and successful people".

His work - like his life - is far richer and stranger than such a verdict suggests. "Puffin" (as his mother nicknamed him, because of his bird-like profile) is one of the most exotic and eccentric characters in British film history. A tiny figure with a fay and gentle manner, he was famous for wearing a blue boiler suit on set, and for sitting cross-legged beneath the camera during shooting. "He dressed like one of the electricians. If anything, he was less well groomed," actress Wendy Hiller recalled of him. Despite his aristocratic background, he was the first British director to join a trade union, serving for 30 years as president of industry body the Association of Cinematograph and Television Technicians (ACTT). In the process, he helped improve pay and conditions for workers, and played a key role in the battle to prevent the government closing down film production during the second world war. "He was a unique and indispensable figure in the British cinema," observed Harold Wilson after Asquith's death in 1968.

Actors and technicians revered Asquith. "He was delightful, charming as a man. To me, he was the best director I have ever worked with," says Jean Kent, one of the leading British stars of the 1940s, who made three films with him. Otto Plaschke, second assistant director on his 1958 feature, Orders to Kill, agrees: "Everybody adored Puffin. He was the most enchanting man."

Ironically - given the attacks made on him because of his aristocratic upbringing - Asquith's motivation for entering the industry was partly to escape his background, to get away from his ambitious family. "Puffin had a difficult life," recalls family friend Jonathan Cecil. "He was a repressed homosexual and he had a difficult relationship with his mother Margot, who was very possessive... he grew up in this ultra-sophisticated world where everyone was worldly and rich."

Passionate about cinema since his student days, Asquith was steeped in the work of the Soviet masters, Pudovkin and Eisenstein, and of the German expressionist film-makers. He had met Proust. He was a brilliant musician. In the mid-1920s, he had even gone to Hollywood to see at first hand how the studios operated. With such a background, it was little wonder his career quickly blossomed. In the late silent era, he was regarded as the equal of Hitchcock and René Clair. "He has all (their) qualities of observation and humour," John Grierson wrote of him. "He has a sense of movement. He has at least equal intelligence. His sense of fun is not so much less as different."

Films such as Shooting Stars (1927) and A Cottage on Dartmoor (1929) are so flamboyant that they make Thomson's criticism of him as an anonymous journeyman seem absurd. The former is a heady melodrama set in the film world. Annette Benson plays the Clara Bow-like vamp, Mae Feather, a film star who pretends to her devoted public that she is happily married to fellow actor Julian (Brian Aherne), when in reality she is having an affair with his best friend (Donald Calthorp). When Julian discovers she has been cheating on him, she tries to kill him by substituting a live bullet for a blank in the gun they are using on set. (In one shot, anticipating Roeg and Cammell's Performance, we see a close-up of a bullet spiralling through the air.) Somehow, the gun is whisked off to the adjoining stage, where a comedy starring Calthorp is being filmed. Inevitably, he is the one who is shot and killed as he performs a stunt on a chandelier. Mae's career collapses in ignominy and, by the final reel, she is eking out an existence as an extra. Julian, by now a famous director, will have nothing to do with her.

What is exhilarating about Shooting Stars is Asquith's delight in his medium: his use of elaborate tracking and crane shots and editing tricks. There is also plenty of satirical humour at the expense of studio bosses and star-struck journalists.

A Cottage on Dartmoor, another embroiled melodrama about a love triangle, is even more extravagant. This tale is of a jealous barber who tries to kill the farmer who steals his girl. In one impressive montage sequence, we see him sharpening a razor between shots of heavy artillery, a few frames into which the screen turns red and cuts to a bottle crashing on the floor as the razor pierces the farmer's neck. Another bravura montage sequence is set inside the local cinema: Asquith shows the faces of an audience marvelling at "the talkies". (The film was planned as a silent film, but a short dialogue sequence was added when it was released.)

Surprisingly, the young director's career stuttered in the 1930s. "The presence of a soundtrack suddenly made Asquith's characters seem unappealingly fay in contrast to the apparently classless stars of the American cinema," historian Nick Thomas noted. Only with Pygmalion (which he co-directed in 1938 with Gabriel Pascal) did his star rise again. As befits the son of Herbert Asquith (the original "Squiffy"), he became a heavy drinker. By the beginning of the war, his alcoholism was a serious worry to friends and collaborators like producer Anatole de Grunewald and Terence Rattigan. There were stories of him falling down drunk in the street and falling asleep in his soup. Somehow, he kept working.

During the 1940s, when his drinking was at its heaviest, he made some of his finest films. There was, for example, The Way to the Stars (1945), a slow-burning drama about RAF men and their American counterparts that was voted the most popular film of the war years. It is easy now to mock the phlegmatic way in which pipe-smoking officers like those played by Michael Redgrave and John Mills react to their colleagues dying ("Bad show, isn't it" is one of their more expressive lines). The understated direction is very different from the expressionism of Asquith's silent films. This is a war picture in which there are no battle sequences beyond the occasional air raid and crash landing. Still, as Dilys Powell noted in her review, the film captures "the emotion behind the laconic phrase ... It holds for anyone who has lived through the years of air battle over England an incomparable quality of regret for the massacre of youth."

While making The Way to the Stars, Asquith struck up one of the more unlikely friendships of his life with Joe Jones, owner of a transport cafe in Catterick, who subsequently employed him as a dishwasher and waiter. "He used to serve the lorry drivers at breakfast time," Jonathan Cecil says. "They [Joe's family] were a kind of surrogate family to him. Joe helped Puffin to kick the alcohol."

Between his stints at Joe's cafe, Asquith was making films such as The Importance of Being Earnest and The Winslow Boy. He was also trying to curb his drinking at a notoriously tough "drying-out" clinic. Even here, Cecil recalls, his trademark courtesy did not desert him. "They'd bring him a bowl of whisky with vinegar in it so it would make him nauseous. They had all these fighting drunks, cursing and being held down, and they'd bring this bowl of revolting muck for him to drink and he'd say, 'Oh, my dear ... that's so kind.' "

By making adaptations of Rattigan, Oscar Wilde and Bernard Shaw plays, Asquith ensured that he would be pigeonholed as a purveyor of tasteful, middlebrow fare. The influential critic Raymond Durgnat coined the phrase "Rattigasquith" to dismiss these literary adaptations. At times, as he marshalled such famously difficult stars as Edith Evans, Richard Burton, Elizabeth Taylor, Orson Welles and Sophia Loren through their paces, he seemed more of a diplomat than an artist. His directorial signature, so evident in Shooting Stars (in which he even has a Hitchcock-style cameo), had become impossible to trace in celebrity-saturated movies such as The Yellow Rolls-Royce and The VIPs. "So unobtrusive is Asquith's direction that we are hardly aware of his part in the collaboration," one critic noted. This, though, was the price that he had to pay to keep working. "He wasn't what is called a star-fucker, but he accepted that stars were an essential ingredient in making a film happen," Plaschke notes.

In their own unfussy way, Asquith's best movies are superbly crafted. The Importance of Being Earnest, for example, works so well precisely because he doesn't try to open up the material for the screen. Calling it "an artificial comedy of the theatre", he celebrates rather than disguises its stage origins. He also elicits exemplary performances from Margaret Rutherford (to whom he once fed whisky to calm her nerves), Redgrave and others. "He had a marvellous way of coaxing what he wanted out of you," Jean Kent says. She, at least, is convinced that he is woefully undervalued. "I don't think he was ever given his due ... not that his reputation ever mattered to him."

· The Anthony Asquith season is at the National Film Theatre, London SE1, until March 31. Box office: 020-7928 3232.